The Laws of Exponents

Exponents exponent Power base 53 means 3 factors of 5 or 5 x 5 x 5

#1: Exponential form: The exponent of a power indicates The Laws of Exponents: #1: Exponential form: The exponent of a power indicates how many times the base multiplies itself. n factors of x

#2: Multiplying Powers: If you are multiplying Powers with the same base, KEEP the BASE & ADD the EXPONENTS! So, I get it! When you multiply Powers, you add the exponents!

Exponent patterns Rule: na•nb = na+b Multiplication Rule What rule can you identify from the following examples? 52•53= _____ =55 34 •32 = ____ =36 28 •26= ____ =214 Rule: na•nb = na+b Multiplication Rule When you multiply two powers that have the same base, add the exponents and keep the base

Why does the multiplication rule work? na•nb = na+b 52 • 53 (5•5) • (5•5•5) 5•5•5•5•5 55

Simplify using exponents: 72•73 95 •93 36 •3-1 = ____ = ___ = ____ = ___ = ____ = ___

#3: Dividing Powers: When dividing Powers with the same base, KEEP the BASE & SUBTRACT the EXPONENTS! So, I get it! When you divide Powers, you subtract the exponents!

Exponent patterns Rule: na  nb = na-b Division Rule What rule can you identify from the following examples? 5451 = _____ =53 89  82 = _____ =87 66 62 Rule: na  nb = na-b = _____ =64 Division Rule When you divide two powers that have the same base, subtract the exponents and keep the base

Why does this rule work? na  nb = na-b 35 32 3•3•3•3•3 3•3 33

Simplify using exponents: 78÷73 95 ÷91 69 ÷6-5 = ____ =___ = ____ =___ = ____ = ___

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#4: Power of a Power: If you are raising a Power to an exponent, you multiply the exponents! So, when I take a Power to a power, I multiply the exponents

Exponent patterns Rule: (na )b = na*b Power Rule What rule can you identify from the following examples? (54)1 = _____ =54 (89)2 = _____ =818 (32)5 = _____ =310 Rule: (na )b = na*b Power Rule When you take the power of a power, multiply the exponents and keep the base

(52 ) 3 52•52•52 52+2+2 56 Why does this rule work? Rule: (na )b = na*b (52 ) 3 52•52•52 52+2+2 56

Simplify using exponents: (142 ) 5 (84 ) 11 (6-5 ) -4 = ____ = ___ = ____ =___ = ____ = ___

#5: Negative Law of Exponents: If the base is powered by the negative exponent, then the base becomes reciprocal with the positive exponent. So, when I have a Negative Exponent, I switch the base to its reciprocal with a Positive Exponent. Ha Ha! If the base with the negative exponent is in the denominator, it moves to the numerator to lose its negative sign!

#6: Zero Law of Exponents: Any base powered by zero exponent equals one. So zero factors of a base equals 1. That makes sense! Every power has a coefficient of 1.

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#7: Product Law of Exponents: If the product of the bases is powered by the same exponent, then the result is a multiplication of individual factors of the product, each powered by the given exponent. So, when I take a Power of a Product, I apply the exponent to all factors of the product.

#8: Quotient Law of Exponents: If the quotient of the bases is powered by the same exponent, then the result is both numerator and denominator , each powered by the given exponent. So, when I take a Power of a Quotient, I apply the exponent to all parts of the quotient.

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